2 Answers
2

Arrows can be purchased from Blacksmiths in limited quantities. Arrow strength is contingent upon Character Level. Arrows in larger
quantities can be purchased from Fletcher in Solitude or The Drunken Huntsmen in Whiterun.

With the implementation of the Dawnguard add-on, arrows can now be crafted at a blacksmith's forge.

Arrows are notably farmed from guards doing target practice (though they only use steel arrows)

to add onto this: once you've obtained a certain type of arrow, you can farm it by reverse pickpocketing that type of arrow onto the guards practicing archery in Solitude. They'll shoot unlimited numbers of those arrows at their targets, which you can then go and pick out at your leisure.
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voxanimusNov 12 '12 at 9:56